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It's become more of a study than a story, to me. I must admit that the background does not necessarily add to the 'story'. A bit like a short chapter at the end of a book which charts what happened to the main characters...except that this is half the book.
markyp-
Yes, that's why I recommended reading it later. The Appendices were put together because of the flood of letters Tolkien and his publisher received, especially in the 60s when the success of LotR became a global phenomenon, that asked for more information about all the tantalising glimpses into the past that occur in the book. There are now much better sources of information available if you're interested in the same things as those letter-writers. If you only wanted to read LotR and not immerse yourself in Middle-earth any further, you can safely stop now.
Oliver Schick
Yes (the Appendices, though). However, if you want to get into Middle-earth more fully, I'd recommend taking a break from the LotR here and turning to the 'Silmarillion' (if you haven't read that yet). The Appendices were intended by Tolkien to give some background to the LotR so people could understand how deeply-rooted in history the story was, and they were also, frankly, a gathering-place for some ancillary material that Tolkien didn't have a story for. The 'Silmarillion' has flaws (well-documented by Christopher Tolkien in the History of Middle-earth series), but is probably a better place to continue than the Appendices, which give tantalising glimpses at the Silmarillion material. I'd recommend reading the 'Silmarillion' together with 'The Atlas of Middle-earth' by Karen Wynn Fonstad (good maps that make what happens a lot clearer).
Alternatively, you could try getting on with some of the recent editions by Christopher Tolkien of the Great Tales of the First Age--'The Fall of Gondolin', 'The Children of Húrin', 'Beren and Lúthien'. These are not fully-formed books but compiled from drafts wholly or partially published before, but re-edited. 'The Children of Húrin' is Tolkien's second-best dramatic idea, after LotR, I think (as I said, not fully-written, but comprehensible with a bit of thought).
Obviously, if you don't want to get into it that heavily, feel free to read the Appendices next. The above recommendations are really just for a different order, as the Appendices came out before a lot of other material that I think it is best to read first.